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Shrinkage-Based Regressions with Many Related Treatments

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  • Enes Dilber
  • Colin Gray

Abstract

When using observational causal models, practitioners often want to disentangle the effects of many related, partially-overlapping treatments. Examples include estimating treatment effects of different marketing touchpoints, ordering different types of products, or signing up for different services. Common approaches that estimate separate treatment coefficients are too noisy for practical decision-making. We propose a computationally light model that uses a customized ridge regression to move between a heterogeneous and a homogenous model: it substantially reduces MSE for the effects of each individual sub-treatment while allowing us to easily reconstruct the effects of an aggregated treatment. We demonstrate the properties of this estimator in theory and simulation, and illustrate how it has unlocked targeted decision-making at Wayfair.

Suggested Citation

  • Enes Dilber & Colin Gray, 2025. "Shrinkage-Based Regressions with Many Related Treatments," Papers 2507.01202, arXiv.org.
    • Handle: RePEc:arx:papers:2507.01202
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